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Re: The Fatal Achilles Heel of Einstein's Relativity

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Thomas 'PointedEars' Lahn wrote:

> alsor@interia.pl wrote:
>> where v is a relativistic speed (a fictitious number):
>> v = vs-vr / 1-ve*vs; (c=1)
> 
> Wrong.  As you could also have read in what I referred you to, the correct
> equation for the relativistic Doppler effect is
> 
>   v_observed = v_source √(1 − (v∕c)²)∕√(1 − v∕c)                       (1)
                                        ^
There is a square root too many in the denominator; it has to be

  v_observed = v_source √(1 − (v∕c)²)∕(1 − v∕c)                          (1)

> or
> 
>   v_observed = v_source √(1 + v∕c)∕(1 − v∕c))

This is therefore correct.

> where v is the *relative speed* of source and observer (positive if the
> source is approaching the observer).

> (Notice those *square roots*?  They are *missing* from *all* your 
> "formulas", from which one can see *at a glance* that you have _not_ 
> applied the Lorentz transform *correctly*.)

I concede that you *had* square roots; but you had them *wrong*:

>> sqrt[(1 - v)/(1 + v)];

See below.
 
> And if you prefer to use natural units (c := 1) – although you are clearly
> not understanding them –, then it becomes
> 
>   v_observed = v_source √(1 − v²)∕√(1 − v)

So this becomes

  v_observed = v_source √(1 − v²)∕(1 − v)

> or
> 
>   v_observed = v_source √(1 + v)∕(1 − v))
                           ^
Still correct, but a parenthesis is missing here:

    v_observed = v_source √((1 + v)∕(1 − v))

(Note that there is a *plus* in the numerator and a *minus* in the 
denominator where you had it *vice-versa*.)

> (and the square roots *are still there*).
> 
> Even if, just for fun, we solve equation 1 for v, we get
> 
>   v = c

Not anymore.

> and
> 
>   v = c v_observed²∕v_source² − c

This becomes

  v = c (v_observed² − v_source²)/(v_observed² + v_source²)

> so for c := 1:
> 
>   v = 1

Not anymore.

> and
> 
>   v = v_observed²∕v_source² − 1,

So,

  v = (v_observed² − v_source²)/(v_observed² + v_source²). ∎

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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The Fatal Achilles Heel of Einstein's Relativity Pentcho Valev <pvalev@yahoo.com> - 2016-11-24 03:49 -0800
  The Fatal Achilles Heel of Einstein's Relativity "David (Lord Kronos) Fuller" <fuller.david@hotmail.com> - 2016-11-24 04:33 -0800
  Re: The Fatal Achilles Heel of Einstein's Relativity Tom Roberts <tjroberts137@sbcglobal.net> - 2016-11-24 09:46 -0600
    Re: The Fatal Achilles Heel of Einstein's Relativity Dusty Kollmann <uberdrivery@uberdriver.info> - 2016-11-24 20:43 +0000
      Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-25 17:46 +0100
        Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-11-25 14:04 -0800
          Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-26 00:20 +0100
            Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-26 01:56 +0100
            Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-11-25 17:18 -0800
              Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-26 02:49 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-11-26 08:46 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-26 19:30 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-11-26 12:37 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-27 13:19 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-27 16:54 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-11-27 12:08 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Dirk Van de moortel <dirkvandemoortel@hotspam.not> - 2016-12-03 11:05 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-12-03 09:51 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Dirk Van de moortel <dirkvandemoortel@hotspam.not> - 2016-12-04 09:44 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-12-04 09:07 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Gary Harnagel <hitlong@yahoo.com> - 2016-12-04 09:17 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-12-04 09:48 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Gary Harnagel <hitlong@yahoo.com> - 2016-12-04 15:39 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-12-05 12:31 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Gary Harnagel <hitlong@yahoo.com> - 2016-12-05 13:23 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-11-27 11:08 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-27 21:29 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-11-27 13:34 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-27 23:42 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-11-30 09:13 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-11-30 19:26 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity Odd Bodkin <bodkinodd@gmail.com> - 2016-11-30 12:51 -0600
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-12-01 14:35 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-12-01 14:42 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity Odd Bodkin <bodkinodd@gmail.com> - 2016-12-01 10:06 -0600
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-12-02 16:40 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity Odd Bodkin <bodkinodd@gmail.com> - 2016-12-02 09:52 -0600
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-12-02 18:45 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity Odd Bodkin <bodkinodd@gmail.com> - 2016-12-02 10:37 -0600
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-11-30 11:03 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-12-01 14:21 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-12-01 15:25 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity Julian Alewine <lliian@lliianenpo.org> - 2016-12-01 14:31 +0000
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-12-02 11:15 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Gary Harnagel <hitlong@yahoo.com> - 2016-12-02 12:17 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-12-03 09:47 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Gary Harnagel <hitlong@yahoo.com> - 2016-12-03 09:56 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-12-03 10:49 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Gary Harnagel <hitlong@yahoo.com> - 2016-12-03 10:58 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity alsor@interia.pl - 2016-12-03 11:31 -0800
                Re: The Fatal Achilles Heel of Einstein's Relativity Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-12-02 22:18 +0100
                Re: The Fatal Achilles Heel of Einstein's Relativity moroney@world.std.spaamtrap.com (Michael Moroney) - 2016-12-01 17:30 +0000
  Re: The Fatal Achilles Heel of Einstein's Relativity Pentcho Valev <pvalev@yahoo.com> - 2016-11-24 15:51 -0800
    Re: The Fatal Achilles Heel of Einstein's Relativity Gary Harnagel <hitlong@yahoo.com> - 2016-11-24 16:15 -0800

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